unit matrix

There is exactly one identity matrix for each square dimension set.

It is consequently a square root of the identity matrix.

Nucleotide sequences use the identity matrix for the same purpose.

The second matrix is the identity matrix and has no effect on the product.

Imagine a simple loop that sets an array to the identity matrix.

This is equivalent to saying that A times its transpose must be the identity matrix.

Let the noise vector be normally distributed as where is an identity matrix.

It can be verified that the above set of points has mean and covariance (the identity matrix).

I is the identity matrix of size n.

The identity matrix has nothing but zeroes except on the main diagonal, where there are all ones.

Columns of the identity matrix are added as column vectors for these variables.

The covariance matrix of T will be the identity matrix.

The Euclidean metric is a special case, where is the identity matrix.

In fact, these four rows are linearly independent and form the identity matrix (by design, not coincidence).

The formula defines a translation if and only if A is the identity matrix.

It has an alternative basis given by the identity matrix and the three Pauli matrices.

More than that was the fact that the system monitor registered his identity matrix intact.

Because is a rotation matrix, where is the identity matrix.

Here is the identity matrix of the same dimension as , and is a real, positive number.

In these equations denotes where is the identity matrix of dimension .

Thus a derived function to return an identity matrix:

The error is minimized when is a scaled identity matrix.

Finally, for any positive integer , denotes the identity matrix.

Every square dimension set of a matrix has a special counterpart called an "identity matrix".

The identity matrix I and any square zero matrix are diagonal.

Note that the term unit matrix is sometimes used to mean something quite different.

Next, let be the unit matrix with the addition of an element k in the position.

Let this be written, the unit matrix.

Let the canonical form of reliability data be a 3-coder-by-15 unit matrix with 45 cells:

Despite the name, matrix units are not the same as unit matrices or unitary matrices.

Because one can divide the top and bottom of the transformation by we lose no generality by setting to the unit matrix.

In the special case where C is the 1-by-1 unit matrix, this identity reduces to the Sherman-Morrison formula.

Let I be the unit matrix with its ith and jth rows interchanged.

Finally, let be the unit matrix with the element substituted for the unit in the i, ith position.

By definition, 1 is the magnitude or absolute value of a unit vector and a unit matrix (more usually called an identity matrix).

Initialise matrix Phi as a 'unit matrix'.

Examples include binary matrices, the zero matrix, the unit matrix, and the adjacency matrices used in graph theory, amongst many others.

Weights would then be given by n coordinates and the sum over all n coordinates has to be zero (because the unit matrix is only auxiliary).

Before Hessian matrix is calculated, initially hessian matrix will include in computation of f(x) as unit matrix.

The unit matrix I is a diagonal matrix of unit elements; a matrix having all its elements zero is said to be null and is written 0.

In linear algebra, the identity matrix or unit matrix of size n is the n x n square matrix with ones on the main diagonal and zeros elsewhere.

However a unit triangular matrix is not the same as the unit matrix, and a normed triangular matrix has nothing to do with the notion of matrix norm.

In the Neglect of Diatomic Differential Overlap (NDDO) method the overlap matrix S is replaced by the unit matrix.

Clearly we cannot normalise X in this case to make both and unit matrices; we say therefore that in this case X is bi-orthogonal or has a generalised orthogonal form.

If U is the unit matrix in the direction of the Higgs field, then the index is proportional to the integral of U(dU) over the (n 1)-sphere at infinity.

Some mathematics books use U and E to represent the Identity Matrix (meaning "Unit Matrix" and "Elementary Matrix", or from the German "Einheitsmatrix", respectively), although I is considered more universal.

In special contexts, the term unit matrix is used as a synonym for "matrix of ones" This is done whenever it is clear that "unit matrix" does not refer to the identity matrix.

(4) Unit matrix - this is the diagonal matrix with units in the diagonal positions; it is written I. (5) Scalar matrix - this is the diagonal matrix with the same scalar quantity, say, in the diagonal positions.

Even though the Cartan subalgebra h is only (n 1)-dimensional, to simplify calculations, it is often convenient to introduce an auxiliary element, the unit matrix which commutes with everything else (which should not be thought of as an element of the Lie algebra!)

It should be noted that if A is Hermitian, then iA is a skew-Hermitian. (13) The isolating vector ei - this vector is the ith column of the unit matrix; it has a unit in the ith element and zeros elsewhere.